In manufacturing products that include precision discrete parts (e.g., microelectronic chips on silicon substrates), controlling manufacturing processes plays a crucial role. Controlling such processes may require, among other things, monitoring the characteristics of manufactured parts (e.g., processed wafers, hereinafter referred to as outputs) and adjusting input parameters accordingly. By adjusting the values of the input parameters, different types of outputs can be produced and the characteristics of the outputs can also be controlled.
For automating the control of the manufacturing processes, a mathematical model of the processing equipment can be used. One example of such a model is called a predictive model. This model is used to predict the future output values (e.g., the characteristics of products) based on historical information (e.g., input parameter values and the corresponding output qualities).
One such predictive model is an offset technique, which is illustrated in FIG. 1. In particular, the values of a number of input parameters 101 are received by an input/output dependency model 103, which calculates a predicted output value y1Pred 105 based on the input values. A corrector 109 then compares the predicted value y1Pred with an actual output value y1a 107 for the given values of the input parameters. If the predicted and actual output values are similar to each other within a certain range, no change is made to the input/output dependency model 103. If the predicted and actual output values are different (e.g., outside the range) from each other, the predictor input/output dependency model 103 is modified by adjusting an offset value (O1) 111 based on the magnitude of the difference.
In equipment that has more than one output, at least some of the outputs may include mutual (shared) inputs. This means the output values of the equipment are not completely independent from each other (e.g., changing an input to adjust a given output may unintentionally change the characteristics of other outputs). In a conventional modeling technique, each output has its own correction system as if the output values are independent from each other. Because the dependencies between the different outputs are not accounted for by the conventional technique, it does not always lead to accurate predictions. In addition, adjusting one offset of one output can affect other outputs.